Radar arrays are typically designed and/or optimized for a specific wavelength range. Arrays are typically composed of identical antenna elements arranged in a regular pattern, such as rectangle. Antenna element spacing is typically chosen to be on the order of half-wavelength at the operating frequency. This permits a large angular scanning range and avoids grating lobes, which occur in spurious directions where the received signals are out of phase by a non-zero integral number of wavelengths.
Certain new radar applications, however, benefit from wideband signals for which traditional arrays are not optimal. With wideband radar it is impossible to satisfy the half wavelength condition for all frequencies in the band, since the spacing between elements may be on the order of half-wavelength at the lowest operating frequency of the array, but is one wavelength at twice the lowest frequency, two wavelengths at four-times the lowest frequency, and so forth. As a result, at higher frequencies there is a directional ambiguity, or in case of near-field microwave imaging (such as in medical applications) an under-utilization of the spatial resolution achievable at the different frequencies.
The design of wideband antenna arrays thus poses several difficulties. One difficulty involves designing small wideband antenna elements having a minimum gain in all frequencies of interest. Another difficulty relates to antenna element size. Antenna element and array sizes are dictated by the lower edge of the band covered. As a result, the array density is sub-optimal for the upper edge of the band.
Among the new applications which can benefit from wideband radar are medical imaging techniques for mapping the interior of the human body and detecting anomalies such as malignant tumors, particularly in breast tissue. Microwave imaging of the human breast has been of interest, both in view of its medical and social importance, and in view of the relatively low-loss materials of the breast.
Signals used for scanning the human body typically occupy frequencies from about 10 MHz to 10 Ghz. Particular attention has recently been drawn to the 3.1 to 10.6 GHz range, which allows license-exempt ultra-wideband (UWB) operation at low signal levels. There is an advantage to using lower frequencies in view of better penetration into the human body, but higher frequencies are desirable in view of their shorter wavelength and better spatial resolution. Use of wideband radar allows high temporal resolution, facilitating discrimination of features according to their depth (distance from the antenna array). The maximum frequency of the signal determines the image resolution, but using only high frequencies is not adequate, due to their low penetration and on account of the appearance of artifacts related to phase ambiguity. It is thus beneficial to use a wide range of frequencies.
Other restrictions on microwave imaging include the need to penetrate the outer attenuating layers of the human body in order to identify underlying features. The faint variations in signal reflection from underlying features are typically masked by reflections from the antenna elements themselves and the tails of reflections from closer features, such as the interface with the skin. Current techniques for overcoming these problems include: calibrating the antenna arrays; cancelling out the contribution of surface layers so as not to interfere with detecting the interior features; and algorithms for reconstructing the spatial map of dielectric properties of the object from multi-antenna element observations. Current algorithms include basic “delay-and-sum” (DAS) algorithms, as well as more intricate inverse-problem algorithms. Nevertheless, current methods still suffer from residual errors and limited dynamic range.
One of the shortcomings of basic DAS algorithms, as well as other current reconstruction algorithms, is that they assume antenna elements to be perfectly isotropic, and that signal paths are lossless. In practice, however, antenna elements have direction-dependent radiation patterns as well as frequency-dependent gains and phase shifts. Practical implementations of current reconstruction algorithms, therefore seek to cancel out these effects by a pre-processing stage that is separate from the reconstruction algorithm itself, e.g., by calibrating the antenna elements and dividing or de-convolving the measured signals by reference calibration signals containing the antenna element gain and phase shift. However, separating the calibration from the image reconstruction is sub-optimal and increases noise and artifacts. For example, if one of the antenna elements receives the target object reflection faintly due to a null in its radiation pattern, pre-calibration techniques merely compensate by over-amplifying the weak signal (along with its noise and artifacts), whereas the appropriate response is to simply ignore the signals from this antenna element.
An additional problem arises on account of path loss caused by propagation in space as well as signal attenuation in the target medium, where the signals arriving from an arbitrary point in the medium to the antenna array arrive at different gains. As noted previously, if this gain is cancelled out before applying the DAS algorithm, then noise amplification may result. Other sources of gain and phase variations in the system include its electrical components (transceivers, mixers, cables, etc).
Another type of phase variation is created by frequency variation in the relative electrical permittivity (∈r) of the medium. This leads to dispersion, where different frequencies have different propagation velocities in the medium.
In general, various frequency-dependent effects contribute to variability in signal amplitude and phase shift according to frequency. In addition, some of these effects (such as antenna array and element radiation pattern, frequency dependence of ∈r) affect amplitude and phase shift according to target object location and signal path, and therefore cannot be cancelled separately.